An archetype and scaling of developmental tissue dynamics across species

Morphometric studies have revealed the existence of simple geometric relationships among various animal shapes. However, we have little knowledge of the mathematical principles behind the morphogenetic dynamics that form the organ/body shapes of different species. Here, we address this issue by focusing on limb morphogenesis in Gallus gallus domesticus (chicken) and Xenopus laevis (African clawed frog). To compare the deformation dynamics between tissues with different sizes/shapes as well as their developmental rates, we introduce a species-specific rescaled spatial coordinate and a common clock necessary for cross-species synchronization of developmental times. We find that tissue dynamics are well conserved across species under this spacetime coordinate system, at least from the early stages of development through the phase when basic digit patterning is established. For this developmental period, we also reveal that the tissue dynamics of both species are mapped with each other through a time-variant linear transformation in real physical space, from which hypotheses on a species-independent archetype of tissue dynamics and morphogenetic scaling are proposed.

organism (e.g cartilage condensation, gene expression?)Line 487 H2O2 Line 499 I'm still not understanding what you mean by dorsal ventral boundary: the mesenchyme does not really have such a boundary (unlike the epithelial AER?) -does this mean cells were labelled in the centre relative to the DV axis, where lmx1b positive and negative cells meet?Could you perhaps illustrate this better with a figure?Line 669 Gene names in italics Figure 1: I find this legend to be a bit overlong, it should really be re-written to just describe what is shown and the rest can be incorporated into the text?In particular, having a study aim in the legend seems out of place.
Figure 2 The Xenopus A-P axis is posturally inverted: shh marking the ZPA clearly shows this for the stages of this study: Endo et al 1997 PMID: 9186057, Keenan and Beck 2016 PMID: 26404044, Wang et al 2015 PMID: 26527308.I can see you've inverted the limbs in this figure to account for this but it should be stated.I'm not clear on how the maps are made-1D or is information captured from multiple layers and stacked?If the former then how do you account for cells that move or divide dorsoventrally in the mesenchyme? Figure 3 rather than using left and right, fro C and D maybe label all the panels ?In the legend, the final statement "Note that the dynamics for the prospective autopod and zeugopod are compared" at the end does not seem to obviously relate to anything shown in the figure ?Reviewer #2 (Remarks to the Author): The goal of the paper is to explore whether there are conserved 'archetypal' growth dynamics in organs detectable among species.The authors produce tissue deformation maps through developmental stages of chick and Xenopus for comparison.For comparisons of tissue dynamics among species, they propose rescaling tissue deformation and synchronizing developmental clocks.They conclude that chicks and xenopus share A-P axis asymmetry, as well as the pattern of cell division contributing to elongation of the limb bud.
The study is a valuable contribution to the limb development in describing details of shape change and dynamics over ontogeny and attempting to devise a method for comparisons that helps to understand underlying principles.
My main comments here are about this study's comparison of species.The study lacks a necessary discussion of anuran limb development as qualitatively different than amniotes (chick), first because anuran limb development derives from different tissues and by a different initiating process.The elongation of the frog limb may indeed independently recapitulate the amniote limb developmental characteristics, but the fundamental developmental difference of having the thyroid-dependent metamorphosis in frogs drive limb initiation, rather than limb buds derived from the early axis/embryonic lateral mesoderm, is not mentioned.
Secondly, the authors conclude -line 403 -"the spatiotemporal expression patterns of hox genes essential for limb development were also found to be conserved" I wonder about this, as the anuran hind limb zeugopod to autopod boundary is complicated by the proximal tarsal modification into an additional hindlimb segment; along with this morphology, the HoxA11-HoxA13 boundary distinguishing the zeugopod is modified.See: Blanco, M. J., Misof, B. Y., Wagner, G. P., Blanco, M. J., Misof, B. Y., & Wagner, G. P. (1998).Heterochronic differences of Hoxa-11 expression in Xenopus fore-and hind limb development: evidence for lower limb identity of the anuran ankle bones.Development genes and evolution, 208(4), 175.
" Cameron and Fallon (1977) noted how the patterns of digit formation of amphibians differed from that of amniotes.In amphibians, there are no interdigital zones of massive cell death during digit formation.Rather the digits appear to arise by differential proliferation of interdigital and digital cells.Each digital primordium first grows and enlarges, and then it segments to form the interphalangeal joints and the precise number of phalanges (Sanz-Ezquerro and Tickle, 2003).In amphibians and lizards, this process seems to be different from mammals and birds because, even when phalanges differentiate by segmentation, there is no continuous primordium dividing up into as many phalanges.Instead, phalanges appear as cartilaginous condensations that grow in size and then segment to form the next phalange in a proximo-distal direction (Fig. 6)." All these features would affect the shape dynamics described.Given that the purpose of the paper is to provide a method for comparing species differences, the acknowledgement of the fundamental differences of highly derived forms requires a review of evidence for homology as a starting point.The differences in gross developmental contexts shouldn't be ignored.
That said, I think this study could potentially provide evidence for similar tissue dynamics *in spite of* the big differences between anurans and chicks, and this discussion is completely missing.For example, if a mouse and chick were compared, there is a strongly supported developmental homology that is 'tinkered' with to create the differences among species, so that the tissue dynamics synchronization is more easily interpretable for similarity and difference from an evolutionary perspective.However, if they find similarities between amniote and anuran limb development, it possibly says more about a deeper question of how evolution is constrained by tissue dynamics even in the case where the 'limb program' is redeployed in a different context (i.e., the post-larval metamorphosis).I would think this is especially important for the stated goal of finding "archetype" forms for organs.(I think they are really assessing is an archetypal ontogeny, not just the resulting form..?) What an archetype is begs some other questions, which would be worthwhile to present here.Why are they similar?Any tissue dynamics-based archetype description would need additional discussion of biophysics as a mechanistic contribution adding to this primarily morphological comparison.It could strengthen the discussion.
The conclusion that the pattern of cell division ("cell flow") contributing to elongation of the limb bud is an important point overall as it contradicts the paradigm that the distal cells are where elongation primarily arises.Also see Young, J. J., & Tabin, C. J. ( 2017).Saunders's framework for understanding limb development as a platform for investigating limb evolution.Developmental biology, 429(2), 401-408.
Both D'arcy Thompson's and this study are missing the third dimension of shape, which is critical in cartilage condensation initiation and digit development.

Reviewer #3 (Remarks to the Author):
This manuscript presents a timely exploration of a significant research question, namely, how to establish a standard that facilitates quantitative comparisons of tissue dynamics in homologous organs across different species.The strength of this study lies in its proposal of an approach to map morphogenetic dynamics from one organ to another using a space-time coordinate system.These achievements are made possible through the integration of cutting-edge measurement technologies, advanced data analysis techniques, and a solid foundation in mathematical knowledge.The discovery of the conservation of rescaled tissue dynamics in developing limb buds between tadpoles and chicks may not be considered ground-breaking in itself.However, it is crucial to acknowledge the significance of this finding in light of the absence of rigorous scientific evidence until now, primarily due to the lack of the proposed approach utilized in this study.
The presented results are compelling and well-aligned with the scope of this study.The limitations are adequately described, addressing the essential aspects.While I believe the manuscript is generally of high quality, I have a few suggestions for minor revisions that will further improve the clarity and impact of their work.These suggestions should not require additional experiments or major modifications.While additional experiments to test the robustness and extensibility of this approach under perturbations such as small molecule inhibitors or low temperatures could be envisioned, it is understandable that including them may delay the timely publication, which should be avoided.Expanding the Discussion section, as suggested below, will enhance the overall significance of the results.I believe that incorporating these revisions will significantly enhance the manuscript and make it even more impactful.1) While the discussion addresses the interpretation of the results, it is recommended to expand on the potential implications of the methods and findings for future research or practical applications in the field.For instance, the authors briefly mention organoid maturation as a target topic for applicability on line 416, but a more detailed explanation would provide greater clarity to the readers.Suggesting potential applications in more depth would be advantageous for a wide range of readers.Additionally, including a paragraph that highlights the limitations of the study would further enhance its practical implications.
2) There are several suggestions to enhance the clarity and structure of the manuscript.Some statements should be revised to ensure they are within the proper scope.For example, it is important to state in the Abstract that their approach is applicable only a phase when the tissue morphogenesis exhibits simple elongation in the limb bud, as described in the Results section.This will provide readers with a clear understanding of the limitations of the study, as mentioned in my comment #1.Another suggestion is to consider shifting the last section in the Results to the Discussion.This section appears to be more of the authors' views and hypotheses, and may be better suited for the Discussion section rather than being presented as a part of rigid results.
3) Figure 4B: The legend states that the white points indicate the closest chick stage to each Xenopus stage, and the black points indicate the Xenopus to chick stage.However, in Figure 4B, the representation of white and black points seems to be opposite to the description in the legend.Please verify the correctness.4) Figure 4E: The authors mentioned that the choice of initial times for each target affects the level of similarity, but they only show the case when the Xenopus stage is fixed.It would be beneficial to present the results in a round-robin manner, considering different initial times for each target.Also, it would be helpful to provide a brief explanation or interpretation as to why the difference level is smaller at chick stage 21 compared to earlier or later stages.The authors should describe what the error bars represent and provide the number of samples used in the analysis in the legend.5: The authors claim a high degree of similarity in ξ-space (line 353), which is an important result.It would be beneficial to quantify the level of similarity to provide a more quantitative assessment of the observed similarity.6) Materials and Methods, line 441: "All animal handling was performed under appropriate anesthesia ..".It is recommended to provide a detailed description of the anesthesia protocol used in the study for the purpose of reproducibility.

Replies to reviewers' comments
First, we would like to thank all the reviewers for their very valuable comments and questions.We have listed our responses to the individual comments below.

Replies to Reviewer #1's Comments
Reviewer #1 (Remarks to the Author): This is an interesting study attempting to find a common morphometric plan underlying the development of hindlimbs in two vertebrate model organisms which differ in size, shape and developmental timing.It combines mathematical modelling with cell tracking in vivo, and builds on a previous study of the chicken hind limb bud.The study uses a very clever method of labelling many.small groups of cells in the mesenchyme along with mathematical modelling which supports an "archetype" for stage 52 to 54.This stage interval is about 5 days of Xenopus tadpole development (starting 9 days after the buds appear, and finishing as digits begin to condense).At these stages the mesenchyme anterior-posterior axis is well established, and cells fated to form the stylopod, zeugopod and autopod can be identified (Tschumi 1957).Effectively, the study and model covers the period when zeugopodal cartilage elements condense and when digits and interdigits are being defined in the autopod.The latter has been recently shown to be recapitulated in in vitro culture in mice, indicating self-organising ability of the limb bud mesenchyme (Fuiten et el PMID: 36994104)The model is backed up with some nice RNAscope data of anterior posterior marker hox genes.There are also of course more interdigital regions in frog hindlimb (5 digits) vs. chick hindlimb (4 digits) and I can't see this reflected in the model or discussed.
Major: The paper would benefit from some more background into the model to be more accessible to biologist readers.The discussion is brief and includes no citations, so is more a conclusion.I think at the least it would be good to address the limitations of this model in terms of the stages it covers, and perhaps to expand the discussion to include reference to the work of others -e.g.What is known about cell division rate and orientation in these models, or in other vertebrates, and how would this direct morphogenetic growth in a comparable way?Additionally I suggest changes that I think would assist with broad readership appeal as "minor" below.
Reply to Reviewer #1's major comments: Thank you very much for your valuable comments.First, please let us clarify the usage of the term "model".In this study, we used a Bayesian statistical model to reconstruct smooth tissue deformation maps from noisy cell trajectory data, where the term "deformation map" means the positional correspondence of each point within a tissue at different time points or the trajectory of each point by which deformation characteristics can be calculated.Thus, the spatiotemporal patterns of quantified local tissue deformation characteristics (heatmaps in Fig. 2) and the cell flows under the ξ coordinate system (Fig. 3) are real values, not virtual (model) values.In this sense, the difference in the number of digits between species does not need to be accounted for a priori to calculate these quantities.In addition, as stated in the original manuscript, "Anatomically, the interspecies differences in the relative lengths of the tarsals and zeugopods and the number of formed digits begin to appear around tXenopus=53.5 (xenopus) and tChick=27 (chick).Thus, these highly consistent cell trajectories in the -space suggest that temporal changes in the relative positions of cells within the developing tissues are well conserved regardless of the state of cartilage differentiation." After the basic skeletal patterns are formed, species-specific tissue deformation begins to appear.
Regarding this point, we have added the following sentence in the Results section of the revised manuscript: "For example, regarding cell/tissue behavior during digit formation within the paddle-like autopod region, amphibians and amniotes have been reported to have qualitative differences in the rate of cell death in the interdigital zone and in the segmentation processes of digits (31)."Furthermore, the following text regarding the quantified spatiotemporal patterns of tissue deformation characteristics has been added to the Results section: Regarding A-P asymmetric growth, "Further, in our previous study on chick limb development, we showed that this A-P asymmetric area growth rate at the tissue level is quantitatively consistent with the positional dependence of the cell cycle time (14)."Regarding the almost homogeneous elongation rate along the P-D axis, "This fact indicates that, similar to the chick case ( 14), the P-D elongation of a Xenopus limb bud cannot be explained by the classical model that limb bud elongation is caused primarily by proliferation of distal cells (25-27, and see also (24) that nicely reviews the history of "proliferation gradient" model); it should be noted that the factors that drive this anisotropic local tissue deformation remain unknown." We have substantially revised the Discussion section in accordance with the three reviewers' comments.The major modifications are as follows: (i) We have added the following sentences describing the limitations of our methodology (please see the subsection "Representation of space-time information and limitations"): "With respect to time (τ), we propose a method for achieving synchronization of developmental time between species based on geometrical information, i.e., cell flow under the ξ-coordinate system.The method has a limitation that it functions effectively only when the transformation of time coordinates between species adheres to the conditions of being both bijective and continuous.These conditions can be compromised when significant interspecies differences in the flow arise; in the case of chick and Xenopus limb development, (geometrical) synchronization was not possible after the phase when basic digit patterning was established.We should note that this does not necessarily imply only a negative aspect, because the method conversely could also serve to detect the emergence of interspecies differences in tissue dynamics, as shown above." (ii) We have also modified the text regarding future challenges: "In this study, we decomposed a tissue deformation map as the product of the average growth L(t) (i.e., species-specific tissue size and aspect ratio at time t) and the rescaled tissue dynamics 0 ( , )   (Eq. 1) and focused on similarities in the latter.However, how the former, species-specific tissue size, is determined remains a critical issue because it not only satisfies pure scientific interest but also is closely linked to applied research.For example, current organoids can reproduce the differentiated states of individual organs, but remain considerably distant from being fully functional, mature organs of adequate size (37).Identifying the factors that determine interspecies differences in the size of homologous organs will introduce the possibility of regulating the size of immature organoids.A group of genes associated with species differences whose expression patterns are not conserved in the τ-ξ coordinate system will provide clues to elucidate the molecular mechanisms responsible for organ size determination."(iii) The following three items have also been added to the Discussion section in response to suggestions from other reviewers.
"Spatially, positions in the rescaled space (ξ), rather than those on an absolute scale, would be encoded as gene expression vectors in a manner common to different species.Changes in tissue size (or more precisely, average deformation L()) are cancelled out in ξ-space, which allows direct comparison of spatial representations within a tissue at different time points.This perspective will be crucial for advancing the previous theoretical frameworks on positional-information coding in static fields (33, 34) to encompass dynamic scenarios.""As described in the Introduction, the trigger/timing of limb development are very different between chick and Xenopus (Keenan and Beck, Dev.Dyn., 2016).Despite such qualitative differences, it is surprising that tissue dynamics are well conserved, which suggests that the evolution of limb morphogenesis is constrained by common physical processes as well as conserved signaling pathways and gene expression patterns across species.Clearly, such an interdisciplinary understanding is necessary to determine what an archetype of tissue dynamics is (including knowing if an archetype itself really exists).In the context of limb development, clarifying the physicochemical factors responsible for the nearly uniform elongation rate along the P-D axis and asymmetric growth/deformation along the A-P axis, as revealed in our analysis (Figs. 3C-H), will be an important clue to understanding the constraints.""Especially, since three-dimensional (3D) features of organ morphology become more pronounced in the later stages of development, 3D map reconstruction would be critical.In the context of limb development, at stages following the establishment of the skeletal patterning (e.g., after St. 30 in the chick case), the shapes of all digits become more distinct, while simultaneously assuming a more 3D arrangement relative to each other.Thus, extending the analysis to a 3D analysis will be essential for a deeper understanding of species differences in tissue dynamics."

Minor:
Throughout: species names in italics Reply: We have corrected all mentions of species names so that they are in italics.

Abstract: include full species names for both chicken and Xenopus
Reply: We have added this information in the revised manuscript.line 71 I am not familiar with the exact meaning of "tissue deformation" in this context, and think it would be more accessible to wider readership if this was briefly explained.
Reply: Thank you for your comment.We have added a brief explanation of tissue deformation as follows: (original) ... the tissue deformation dynamics during animal development (6).
(revised) ... the tissue deformation dynamics during animal development that include spatio-temporal patterns of area/volume change of each local tissue piece and the extent/direction of its stretching or shrinking (6).

Line 84: similarly, what is a tissue deformation map?
Reply: We have added a brief explanation of a tissue deformation map as follows: (original) … to obtain quantitative tissue deformation maps for the developmental processes of organs… (revised) … to obtain quantitative tissue deformation maps (i.e., the positional correspondence of each point within a tissue at different time points or the trajectory of each point by which deformation characteristics can be calculated) for the developmental processes of organs… Line 114: can you explain why "on the dorsal ventral boundary plane" and what this means?Is the grid focused somehow so that epithelial cells are not triggered to express GFP?The image in figure 2A (and S1) is really nice but I cannot tell if it is mesenchymal only -were two lasers used to focus on a single spot, and only where they meet the heat shock promoter activates?
Reply: Thank you for this comment.For convenience, here we were referring to the frontal section at the mid dorsoventral (D-V) level where the cross-sectional area of a limb bud becomes maximal as the "D-V boundary plane".To avoid any confusion, we have decided not to use the term "dorsalventral boundary" in the revised manuscript.The focus on that plane is because the distinctive event of cartilage formation during limb development occurs around the D-V boundary, not at the dorsal/ventral end.Regarding GFP induction, laser irradiation can be focused to a certain D-V level to some extent, but each spot can become elongated in the D-V direction.However, we found that the shape of each spot was well maintained during our measurement time interval (around 24 hours), and that even if we changed the focus of the microscope in the D-V direction, the spot position hardly changed in the plane spanned by the A-P and P-D axes.This means that the D-V dependence of the in-plane deformation is sufficiently small, at least in the measurement interval.As for this point, we have added the explanation in the Materials and Methods as follows: "Since our aim was to compare the 2D deformation dynamics on the frontal plane at the mid D-V level with the maximal area of a limb bud in Xenopus with that previously reported for chick (14), we focused the irradiation within this plane (Fig. 2A).The heat-shock treatment was performed as described in our previous work (20).The diameter of a single labeled spot on the plane was typically 20-30 μm, a size equivalent to a few cells.Although laser irradiation can be focused to a certain D-V level to some extent, each spot could become elongated in the D-V direction.However, we found that the in-plane shape of each spot was well maintained during our measurement time interval (around 24 hours), and that even if we changed the focus of the microscope in the D-V direction, the spot position hardly changed in the plane.This means that the D-V dependence of the in-plane deformation is sufficiently small, at least in the measurement interval." Line 120/121 state the Nieuwkoop and Faber stages used?
Reply: The staging method we adopted is described in the statement immediately following.In a previous study, we proposed an objective staging method based on the contour shape of a limb bud, and we adopted that method here.This was because the developmental rate of Xenopus, a cold-blooded animal, varies significantly, and there is not always a precise alignment between stage values and actual time.This point was stated in the Materials and Methods: "Staging of each individual was based on a previously proposed morphometric staging method (21); briefly, digitized outlines of the limb buds were approximated using elliptic Fourier descriptors, and a continuous stage value, not discrete values as in traditional staging (e.g., 51 and 52), was assigned to each individual based on its coefficients.In this study, this morphometric stage was denoted by Xenopus t ." Line 135: Xenopus limb bud stages are points on a continuum, but how did you accurately subdivide each stage in to 10th stages?
Reply: As stated above, Xenopus staging was based on a previously proposed morphometric method.
Briefly, digitized outlines of the limb buds were approximated using elliptic Fourier descriptors, and   (14).The only minor modification from the previous study was that we changed the staging method.In the previous study, a tissue deformation map was quantified for every 12-hour interval, and for each time point, we assigned the integer value of the Hamburger-Hamilton stage with a shape closest to that observed at the time point.In the present study, staging was performed using increments of 0.5 (not necessarily integers) based on incubation time." Line 139 citations are needed to support this "Xenopus limb buds include the prospective autopod (toe-to-ankle), zeugopod (lower leg), and stylopod (upper leg) regions.In contrast, chick limb buds contain mainly the former two, while the stylopod is embedded in the trunk.

Reply:
We modified the corresponding sentences as follows: "Xenopus limb buds include the prospective autopod (toe-to-ankle), zeugopod (lower leg), and stylopod (upper leg) regions ( 22).In contrast, as shown later, based on the inverse mapping of cartilage patterns, chick limb buds contain mainly the former two, while the stylopod is embedded in the trunk."

Line 173 gene names in italics
Reply: We have made this correction.
Line 229 "we can intuitively see…" please explain what we are supposed to be seeing because I cannot make this conclusion from the coloured vectors in figure 3C and D. Are there even interdigits present at stage 52?Maybe this refers to another figure?
Reply: Thank you for this comment.The colored vectors represent the movement of the limb bud mesenchymal cells when observed in the ξ coordinate system.What we wanted to state was that, in the internal tissues of a limb bud, both species share a similar flow oriented from the posterior to the anterior side, while the direction of the arrow around the limb bud boundaries (e.g., anterior boundary) is not necessarily similar.We have modified the text as follows: (original) "we can intuitively see that the cell trajectories of the internal tissues that will form future skeletal structures are more consistent between species than those near the tissue boundaries (Fig. 3C, D)" (revised) "we can intuitively see that the cell trajectories (the flow patterns in the ξ coordinate system) of the internal tissues that will form future skeletal structures are more consistent between species (i.e., basically oriented from posterior to anterior) than those near the tissue boundaries (Fig. 3C, D Reply: Thank you for this comment.We introduced the concept of a common clock, which is represented as an abstract one-dimensional curve, and we regarded the developmental stages of each species as time coordinates of the common clock.Then, determining the correspondence of the developmental stages between species (i.e., synchronizing the developmental times) means giving the coordinate transformations between those time coordinates.Here, we devised a method of synchronization (or coordinate transformation) based solely on the geometric information, i.e., tissue deformation dynamics, not on changes in cellular states such as gene expression or cartilage condensation.As shown in Fig. 3, we defined a spatial coordinate system, ξ, in which tissue deformation is represented as a cell flow.We synchronized the developmental time by adjusting the scale interval of the time axis of both species so that the difference between cell trajectories starting from the same initial position was as small as possible.The introduction of mathematical concepts is inevitable for a more precise definition of synchronization.The main text is limited to an intuitive explanation, while the Materials and Methods text provides a more rigorous explanation (please see the subsection "Common clock T and synchronization between species").Regarding this point, the main text states the following: "As a way to find the composite map that relates stages between chick and Xenopus (denoted by Reply: As explained above, here we were referring to the frontal section at the mid dorsoventral (D-V) level where the cross-sectional area of a limb bud becomes maximal as the "D-V boundary plane".
To avoid any confusion, we have decided not to use the term "dorsal-ventral boundary" in the revised manuscript.We have modified Fig. S1 to illustrate this.

Line 669 Gene names in italics
Reply: We have made this correction.Reply: Thank you very much for this comment.We have revised the legend of Figure 1 accordingly.
As you pointed out, we agree that including the study aim is out of place; thus, we deleted it.We then confirmed that the rest of the text corresponds to the figure.Reply: Thank you for this comment.At your suggestion, we have stated the following in the legend of Fig. 2: "Note that the images of the Xenopus limb bud, except for the top-left photo in panel (A), are inverted in the A-P direction to have the posterior side facing downward."

I'm not clear on how the maps are made-1D or is information captured from multiple layers and stacked? If the former then how do you account for cells that move or divide dorsoventrally in the mesenchyme?
Reply: As stated above, we are focusing on the 2D deformation dynamics of mesenchymal tissue on the frontal plane at around the mid D-V level where the cross-sectional area of a limb bud becomes maximal.In addition, even when each spot became elongated in the D-V direction, we found that the shape of each spot was well maintained during our measurement time interval (around 24 hours), and that when we changed the focus of the microscope in the D-V direction, the spot position hardly changed in the plane.This means that the D-V dependence of the in-plane deformation is sufficiently small, at least in the measurement interval.Another important piece of information is that tissue-level deformation is not calculated from the movement of cells within each spot, but from the change in the relative positions among the labeled spots.Therefore, if the relative positional changes between spots over the entire limb bud are reproducible, the deformation dynamics can be correctly reconstructed.
In that sense, our data are highly reproducible among samples, and the resultant reconstructed tissue deformation dynamics are reliable.Regarding the latter point, we have added the following sentences in the Materials and Methods: "It should be noted that tissue-level deformation is not calculated from the movement of cells within each spot, but from the change in the relative positions among the labeled spots.Therefore, if the relative positional changes between spots over the entire limb bud are reproducible, the deformation dynamics can be correctly reconstructed.In that sense, our data are highly reproducible among samples, and the resultant reconstructed tissue deformation dynamics are reliable." Figure 3 rather than using left and right, fro C and D maybe label all the panels ?In the legend, the final statement "Note that the dynamics for the prospective autopod and zeugopod are compared" at the end does not seem to obviously relate to anything shown in the figure ?Reply: According to this comment, we relabeled Fig. 3 (please see Fig. 3 and its legend in the revised manuscript).The final statement, "Note that the dynamics for the prospective autopod and zeugopod are compared" is related to the figure because the flow pattern in the ξ coordinate system changes depending on the region to be analyzed within the limb bud (as analyzed in Fig. 4H).We have slightly modified that sentence as follows: (original) "Note that the dynamics for the prospective autopod and zeugopod are compared."(revised) "The cell flows in the ξ coordinate system shown in panels (C) and (D) correspond to the morphogenesis of the region consisting of prospective autopods and zeugopods."

Replies to Reviewer #2's Comments
Reviewer #2 (Remarks to the Author): The goal of the paper is to explore whether there are conserved 'archetypal' growth dynamics in organs detectable among species.The authors produce tissue deformation maps through developmental stages of chick and Xenopus for comparison.For comparisons of tissue dynamics among species, they propose rescaling tissue deformation and synchronizing developmental clocks.They conclude that chicks and xenopus share A-P axis asymmetry, as well as the pattern of cell division contributing to elongation of the limb bud.The study is a valuable contribution to the limb development in describing details of shape change and dynamics over ontogeny and attempting to devise a method for comparisons that helps to understand underlying principles.

My main comments here are about this study's comparison of species. The study lacks a necessary discussion of anuran limb development as qualitatively different than amniotes (chick), first because anuran limb development derives from different tissues and by a different initiating process. The elongation of the frog limb may indeed independently recapitulate the amniote limb developmental
characteristics, but the fundamental developmental difference of having the thyroid-dependent metamorphosis in frogs drive limb initiation, rather than limb buds derived from the early axis/embryonic lateral mesoderm, is not mentioned.
Reply: First, we would like to sincerely thank you for your very valuable comments.We completely agree that stating the differences in gross developmental contexts is biologically very important in comparing chickens and frogs.We have modified the manuscript to reflect these comments as much as possible.
According to this comment, we have added the following sentences in the Introduction and Discussion sections: (Introduction) "Both species share many developmental characteristics, including major signaling and gene expression patterns, whereas the trigger and timing of development are clearly different.Limb buds of amniotes including chick develop concurrently with the main body axis formation of an embryo and arise from the lateral plate mesoderm.In contrast, limb development in Xenopus proceeds as one of the thyroxine (thyroid hormone)-dependent events in metamorphosis after embryonic stage (17), and the precise origin of a limb bud is difficult to determine (18).Through the comparison of homologous organs with such qualitative differences, we inquired into the existence of archetypal tissue dynamics."(Discussion) "As described in the Introduction, the trigger/timing of limb development are different between chick and Xenopus.Despite such qualitative differences, it is surprising that tissue dynamics are well conserved, which suggests that the evolution of limb morphogenesis is constrained by common physical processes, as well as conserved signaling pathways and gene expression patterns across species.Clearly, such an interdisciplinary understanding is necessary to determine what an archetype of tissue dynamics is (including knowing if an archetype itself really exists).In the context of limb development, clarifying the physicochemical factors responsible for the nearly uniform elongation rate along the P-D axis and asymmetric growth/deformation along the A-P axis, as revealed in our analysis (Figs. 3C-H), will be an important clue to understanding the constraints." Secondly, the authors conclude -line 403 -"the spatiotemporal expression patterns of hox genes essential for limb development were also found to be conserved" I wonder about this, as the anuran hind limb zeugopod to autopod boundary is complicated by the proximal tarsal modification into an additional hindlimb segment; along with this morphology, the HoxA11-HoxA13 boundary distinguishing the zeugopod is modified.See: Blanco, M. J., Misof, B. Y., Wagner, G. P., Blanco, M. J., Misof, B. Y., & Wagner, G. P. (1998).
Heterochronic differences of Hoxa-11 expression in Xenopus fore-and hind limb development: evidence for lower limb identity of the anuran ankle bones.Development genes and evolution, 208(4), 175.
Reply: Thank you for this comment.We read the above paper, and we now have a better understanding of the differences between forelimbs and hindlimbs.In this paper, the expression of HoxA11 in the hindlimb was examined by RNAscope, and we found that the obtained pattern was somewhat different from that examined by ordinary in situ hybridization in the Blanco 1998 paper.For example, in the Blanco 1998 paper, the expression in later stages was very weak, whereas our results show a more regional pattern with a broad, strong signal in the zeugopod.We think that this difference is due to detection sensitivity.Regarding the comparison of expression patterns in chick and Xenopus hindlimbs, as shown in the right panel of Fig. 5B, the range of Hoxa11 expression in ξ-space was very similar in both species, at least when basic limb skeletal patterning was done.In contrast, the somewhat ambiguous overlapping of the Hoxa11 expression ranges between species in the early stages is probably because those stages correspond to the transient period in which the distal end of the Hoxa11 expression region shifts from the tip of limb bud to the more proximal side.
We have added the following sentences in the Results.
synchronization is more easily interpretable for similarity and difference from an evolutionary perspective.However, if they find similarities between amniote and anuran limb development, it possibly says more about a deeper question of how evolution is constrained by tissue dynamics even in the case where the 'limb program' is redeployed in a different context (i.e., the post-larval metamorphosis).I would think this is especially important for the stated goal of finding "archetype" forms for organs.(I think they are really assessing is an archetypal ontogeny, not just the resulting form..?) What an archetype is begs some other questions, which would be worthwhile to present here.Why are they similar?Any tissue dynamics-based archetype description would need additional discussion of biophysics as a mechanistic contribution adding to this primarily morphological comparison.It could strengthen the discussion.
Reply: We appreciate this valuable comment.As described above, according to the comments received, we have added the following sentences in the Discussion section: "As described in the Introduction, the trigger/timing of limb development are very different between chick and Xenopus.Despite such qualitative differences, it is surprising that tissue dynamics are well conserved, which suggests that the evolution of limb morphogenesis is constrained by common physical processes, as well as conserved signaling pathways and gene expression patterns across species.Clearly, such an interdisciplinary understanding is necessary to determine what an archetype of tissue dynamics is (including knowing if an archetype itself really exists).In the context of limb development, clarifying the physicochemical factors responsible for the nearly uniform elongation rate along the P-D axis and asymmetric growth/deformation along the A-P axis, as revealed in our analysis (Figs. 3C-H), will be an important clue to understanding the constraints." The conclusion that the pattern of cell division ("cell flow") contributing to elongation of the limb bud is an important point overall as it contradicts the paradigm that the distal cells are where elongation primarily arises.Also see Young, J. J., & Tabin, C. J. (2017).Saunders's framework for understanding limb development as a platform for investigating limb evolution.Developmental biology, 429(2), 401-408.

Reply:
We have added the following sentence: "This fact indicates that, similar to the chick case ( 14), the P-D elongation of a Xenopus limb bud cannot be explained by the classical model that limb bud elongation is caused primarily by proliferation of distal cells (25-27, and see also (24) that nicely reviews the history of "proliferation gradient" model)" Both D'arcy Thompson's and this study are missing the third dimension of shape, which is critical in cartilage condensation initiation and digit development.
Reply: We agree with this comment.In this study, we analyzed the two-dimensional tissue deformation dynamics of mesenchyme in the frontal plane at around the middle of the D-V axis, where basic skeletal patterning occurs.At stages following the establishment of the skeletal patterning (e.g., after St. 30 in the chick case), the shapes of all the digits become more distinct, while simultaneously assuming a more three-dimensional arrangement relative to each other.Species differences in the morphology and the proportion of anatomical structures will be stronger in later stages, and thus extending the analysis to a 3D analysis will be essential for a deeper understanding of species differences in tissue dynamics.We have added the following text in the Discussion section: "Especially, since three-dimensional (3D) features of organ morphology become more pronounced in the later stages of development, 3D map reconstruction would be critical.In the context of limb development, at stages following the establishment of the skeletal patterning (e.g., after St. 30 in the chick case), the shapes of all digits become more distinct, while simultaneously assuming a more 3D arrangement relative to each other.Thus, extending the analysis to a 3D analysis will be essential for a deeper understanding of species differences in tissue dynamics."

Reply to reviewer #3's comments:
Reviewer #3 (Remarks to the Author): This manuscript presents a timely exploration of a significant research question, namely, how to establish a standard that facilitates quantitative comparisons of tissue dynamics in homologous organs across different species.The strength of this study lies in its proposal of an approach to map morphogenetic dynamics from one organ to another using a space-time coordinate system.These achievements are made possible through the integration of cutting-edge measurement technologies, advanced data analysis techniques, and a solid foundation in mathematical knowledge.The discovery of the conservation of rescaled tissue dynamics in developing limb buds between tadpoles and chicks may not be considered ground-breaking in itself.However, it is crucial to acknowledge the significance of this finding in light of the absence of rigorous scientific evidence until now, primarily due to the lack of the proposed approach utilized in this study.
The presented results are compelling and well-aligned with the scope of this study.The limitations are adequately described, addressing the essential aspects.While I believe the manuscript is generally of high quality, I have a few suggestions for minor revisions that will further improve the clarity and impact of their work.These suggestions should not require additional experiments or major modifications.While additional experiments to test the robustness and extensibility of this approach under perturbations such as small molecule inhibitors or low temperatures could be envisioned, it is understandable that including them may delay the timely publication, which should be avoided.
Expanding the Discussion section, as suggested below, will enhance the overall significance of the results.I believe that incorporating these revisions will significantly enhance the manuscript and make it even more impactful.
Reply: Thank you very much for your positive comments.Below is a list of responses to your suggestions.
1) While the discussion addresses the interpretation of the results, it is recommended to expand on the potential implications of the methods and findings for future research or practical applications in the field.For instance, the authors briefly mention organoid maturation as a target topic for applicability on line 416, but a more detailed explanation would provide greater clarity to the readers.Suggesting potential applications in more depth would be advantageous for a wide range of readers.Additionally, including a paragraph that highlights the limitations of the study would further enhance its practical implications.

Reply:
The Discussion section has been substantially revised in accordance with the comments conserved, which suggests that the evolution of limb morphogenesis is constrained by common physical processes, as well as conserved signaling pathways and gene expression patterns across species.Clearly, such an interdisciplinary understanding is necessary to determine what an archetype of tissue dynamics is (including knowing if an archetype itself really exists).In the context of limb development, clarifying the physicochemical factors responsible for the nearly uniform elongation rate along the P-D axis and asymmetric growth/deformation along the A-P axis, as revealed in our analysis (Figs. 3C-H), will be an important clue to understanding the constraints.""Especially, since three-dimensional (3D) features of organ morphology become more pronounced in the later stages of development, 3D map reconstruction would be critical.In the context of limb development, at stages following the establishment of the skeletal patterning (e.g., after St. 30 in the chick case), the shapes of all the digits become more distinct, while simultaneously assuming a more 3D arrangement relative to each other.Thus, extending the analysis to a 3D analysis will be essential for a deeper understanding of species differences in tissue dynamics." 2) There are several suggestions to enhance the clarity and structure of the manuscript.Some statements should be revised to ensure they are within the proper scope.For example, it is important to state in the Abstract that their approach is applicable only a phase when the tissue morphogenesis exhibits simple elongation in the limb bud, as described in the Results section.This will provide readers with a clear understanding of the limitations of the study, as mentioned in my comment #1.
Another suggestion is to consider shifting the last section in the Results to the Discussion.This section appears to be more of the authors' views and hypotheses, and may be better suited for the Discussion section rather than being presented as a part of rigid results.
Reply: According to this comment, we have modified the manuscript as follows: (i) Regarding the limitation of the proposed method, we have added an explanation in the Discussion section as stated above.We have also modified the Abstract as follows: (original) "...We found that tissue dynamics are well conserved across species under this space-time coordinate system, and that the tissue dynamics of both species are mapped with each other through a time-variant linear transformation in real physical space,..." (revised) "...We found that tissue dynamics are well conserved across species under this space-time coordinate system, at least from the early stages of limb development through the phase when basic digit patterning was established.For this developmental period, we also revealed that the tissue dynamics of both species are mapped with each other through a time-variant linear transformation in real physical space,..." (ii) Secondly, according to the reviewer's suggestion, we have shifted the last section in the Results to the Discussion.Reply: In this revision, we have analyzed the case when the chick stage is fixed.As shown in the original manuscript, we found that chick stage 21 was the best when the Xenopus stage was fixed at 50.6, so in an additional analysis, we fixed the chick stage at 21 and changed the Xenopus stage.As a result, the best agreement of trajectories between species was found at 50.6 (51.1 was equally good).
Therefore, in this study, we chose 50.6 (Xenopus) and 21 (chick) as the initial time combination.Note that as shown in the heatmap in Fig. 4B, the closest chick stage to Xenopus stages 50.6 and 51.1 is 21.This is thought to be because the relative positions of cells within the tissue do not change very much

=50
continuous stage value, not discrete values as in traditional staging (e.g., 51 and 52), was assigned to each sample based on its coefficients.For each individual, the positional coordinates of the fluorescently labeled spots were measured at 2 to 4 time points approximately every 24 hours, and the coordinates at timepoints between the measurements were obtained by linear interpolation.That is, as shown in Fig.S1C, for each sample, we obtained cell trajectory data for a time window represented as a line segment on the number line.Samples containing cell trajectory data within each subdivided interval were used to reconstruct the deformation dynamics during that interval.This point is explained in the Materials and Methods as follows:"Staging of each individual was based on a previously proposed morphometric staging method (21); briefly, digitized outlines of the limb buds were approximated using elliptic Fourier descriptors, and a continuous stage value, not discrete values as in traditional staging (e.g., 51 and 52), was assigned to each individual based on its coefficients.In this study, this morphometric stage was denoted by Xenopus t .Each limb bud was resized to a previously determined typical value corresponding to its morphometric stage.The spatial coordinates of the fluorescently labeled spots were measured at 2 to 4 time points approximately every 24 hours for each individual, and the coordinates at the timepoints between the measurements were obtained by linear interpolation.The period from Xenopus t nine roughly equally spaced time intervals (each interval corresponded to a 0.4-0.5 stage increment), and data from the individuals included in each interval were integrated to reconstruct the tissue deformation map for that interval."Line136 state HH stagesReply: Yes, we based our chick staging on the Hamburger-Hamilton )" Paragraph starting line 236: what criteria did you use/match to set the clock for each organism (e.g cartilage condensation, gene expression?) we aligned the scales of their temporal axes such that the mean difference in cell trajectories from the same initial position in the -space is minimized (see Materials and Methods for details)."Line487 H2O2Reply: We have rewritten this correctly as H2O2.Line 499 I'm still not understanding what you mean by dorsal ventral boundary: the mesenchyme doesnot really have such a boundary (unlike the epithelial AER?) -does this mean cells were labelled in the centre relative to the DV axis, where lmx1b positive and negative cells meet?Could you perhaps illustrate this better with a figure?

Figure 1 :
Figure 1: I find this legend to be a bit overlong, it should really be re-written to just describe what is shown and the rest can be incorporated into the text?In particular, having a study aim in the legend seems out of place.

Figure 2
Figure 2 The Xenopus A-P axis is posturally inverted: shh marking the ZPA clearly shows this for the stages of this study: Endo et al 1997 PMID: 9186057, Keenan and Beck 2016 PMID: 26404044, Wang et al 2015 PMID: 26527308.I can see you've inverted the limbs in this figure to account for this but it should be stated.
3) Figure4B: The legend states that the white points indicate the closest chick stage to each Xenopus stage, and the black points indicate the Xenopus to chick stage.However, in Figure4B, the representation of white and black points seems to be opposite to the description in the legend.Please verify the correctness.Reply: Thank you for this comment.We revised the legend as follows: (Original) "The white and gray points/curve indicate the closest chick stage to each Xenopus stage, which defines the map 1 CX −  .The black and gray points/curve show the closest Xenopus stage to each chick stage, defining the map and gray points/curve indicate the correspondence of each Xenopus stage to the closest chick stage, which defines the map 1 CX −  .The black and gray points/curve show the correspondence of each chick stage to the closest Xenopus stage, defining the map 4E: The authors mentioned that the choice of initial times for each target affects the level of similarity, but they only show the case when the Xenopus stage is fixed.It would be beneficial to present the results in a round-robin manner, considering different initial times for each target.Also, it would be helpful to provide a brief explanation or interpretation as to why the difference level is smaller at chick stage 21 compared to earlier or later stages.The authors should describe what the error bars represent and provide the number of samples used in the analysis in the legend.
In our previous study, we quantified the deformation map for every 12-hour interval.Thus, each heatmap shown in Fig.2Eis the result of each 12-hour interval.Since the developmental rate of chickens, table.A stage value was assigned to each sample using increments of 0.5 (not necessarily integers) based on incubation time.